Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If $u(t,x)\in L^{2}([0,T],H^{2}(\mathbb{R}^{n}))$, $\partial_{t}u \in L^{2}([0,T],L^{2}(\mathbb{R}^{n}))$, prove that $$ u(t,x)\in C([0,T],H^{1}(\mathbb{R}^{n})) $$

share|cite|improve this question
Do you have a PDE that $u$ satisfies? Evans' PDE book has results of this kind. – Albert Altarovici Jan 17 '13 at 11:19
just to be precise, you find the theorem you are looking for on page 288 (Evans, Partial Differential Equation), theorem 4 for a general non negative integer $m$. – user8 Jan 17 '13 at 11:29

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.